{"id":19512,"date":"2024-04-15T05:40:27","date_gmt":"2024-04-15T05:40:27","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=19512"},"modified":"2024-04-15T05:40:27","modified_gmt":"2024-04-15T05:40:27","slug":"a-linear-hamming-code-is-used-to-map-4-bit-messages-to-7-bit-codewords-the-encoder-mapping-is-linear-if-the-message-0001-is-mapped-to-the-codeword-0000111-and-the-message-0011-is-mapped-to-the-code","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-linear-hamming-code-is-used-to-map-4-bit-messages-to-7-bit-codewords-the-encoder-mapping-is-linear-if-the-message-0001-is-mapped-to-the-codeword-0000111-and-the-message-0011-is-mapped-to-the-code\/","title":{"rendered":"A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to A. 0010011 B. 1111111 C. 1111000 D. 1100001"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;10011&#8243; option2=&#8221;1111111&#8243; option3=&#8221;1111000&#8243; option4=&#8221;1100001&#8243; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{A}}$.<\/p>\n<p>A linear Hamming code is a linear code that can correct single-bit errors. It is a $7$-bit code, which means that it can encode $2^7 = 128$ messages. The encoder mapping is linear, which means that the codeword for a message is the sum of the codewords for the individual bits of the message.<\/p>\n<p>If the message $0001$ is mapped to the codeword $0000111$, and the message $0011$ is mapped to the codeword $1100110$, then the message $0010$ is mapped to the codeword $0010011$. This is because the codeword for $0010$ is the sum of the codewords for $0001$ and $0011$, which is $0000111 + 1100110 = 0010011$.<\/p>\n<p>Here is a more detailed explanation of each option:<\/p>\n<ul>\n<li>Option A: $0010011$ is the correct answer. This is because the codeword for $0010$ is the sum of the codewords for $0001$ and $0011$, which is $0000111 + 1100110 = 0010011$.<\/li>\n<li>Option B: $1111111$ is not the correct answer. This is because the codeword for $0010$ cannot be $1111111$, since $1111111$ is not a valid codeword in a $7$-bit Hamming code.<\/li>\n<li>Option C: $1111000$ is not the correct answer. This is because the codeword for $0010$ cannot be $1111000$, since $1111000$ is not a valid codeword in a $7$-bit Hamming code.<\/li>\n<li>Option D: $1100001$ is not the correct answer. This is because the codeword for $0010$ cannot be $1100001$, since $1100001$ is not a valid codeword in a $7$-bit Hamming code.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;10011&#8243; option2=&#8221;1111111&#8243; option3=&#8221;1111000&#8243; option4=&#8221;1100001&#8243; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[685],"tags":[],"class_list":["post-19512","post","type-post","status-publish","format-standard","hentry","category-information-theory-and-coding","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to A. 0010011 B. 1111111 C. 1111000 D. 1100001<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-linear-hamming-code-is-used-to-map-4-bit-messages-to-7-bit-codewords-the-encoder-mapping-is-linear-if-the-message-0001-is-mapped-to-the-codeword-0000111-and-the-message-0011-is-mapped-to-the-code\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to A. 0010011 B. 1111111 C. 1111000 D. 1100001\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;10011&#8243; option2=&#8221;1111111&#8243; option3=&#8221;1111000&#8243; option4=&#8221;1100001&#8243; correct=&#8221;option1&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-linear-hamming-code-is-used-to-map-4-bit-messages-to-7-bit-codewords-the-encoder-mapping-is-linear-if-the-message-0001-is-mapped-to-the-codeword-0000111-and-the-message-0011-is-mapped-to-the-code\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:40:27+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to A. 0010011 B. 1111111 C. 1111000 D. 1100001","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/a-linear-hamming-code-is-used-to-map-4-bit-messages-to-7-bit-codewords-the-encoder-mapping-is-linear-if-the-message-0001-is-mapped-to-the-codeword-0000111-and-the-message-0011-is-mapped-to-the-code\/","og_locale":"en_US","og_type":"article","og_title":"A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to A. 0010011 B. 1111111 C. 1111000 D. 1100001","og_description":"[amp_mcq option1=&#8221;10011&#8243; option2=&#8221;1111111&#8243; option3=&#8221;1111000&#8243; option4=&#8221;1100001&#8243; correct=&#8221;option1&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-linear-hamming-code-is-used-to-map-4-bit-messages-to-7-bit-codewords-the-encoder-mapping-is-linear-if-the-message-0001-is-mapped-to-the-codeword-0000111-and-the-message-0011-is-mapped-to-the-code\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T05:40:27+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-linear-hamming-code-is-used-to-map-4-bit-messages-to-7-bit-codewords-the-encoder-mapping-is-linear-if-the-message-0001-is-mapped-to-the-codeword-0000111-and-the-message-0011-is-mapped-to-the-code\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-linear-hamming-code-is-used-to-map-4-bit-messages-to-7-bit-codewords-the-encoder-mapping-is-linear-if-the-message-0001-is-mapped-to-the-codeword-0000111-and-the-message-0011-is-mapped-to-the-code\/","name":"A linear Hamming code is used to map 4-bit messages to 7-bit codewords. 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